We report both measurements and local density approximation calculations of the Fe K-edge X-ray absorption near edge (XANES) spectra of LnOFeAs high T _c superconductors. Calculations based on the local structure centered at the Fe site obtained by crystallographic investigations reproduce observed changes in the spectra under switching of the crystal structure from the tetragonal to the orthorhombic striped phase. Although the local structure changes are very small, their effect is revealed by clear signatures at the absorption edge, indicating the variations of the Fe local unoccupied electronic states. Calculated Fe density of states that do not include spin ordering in the orthorhombic phase do not show a significant modification, implying that the striped spin ordering in the orthorhombic phase is necessary to describe its electronic properties.